On Product of Spaces of Quasicomponents

Abstract

We use characterization of quasi-components by continous functions to obtain the well known theorem which states that product of quasi-components $Q_x,Q_y$ of topological spaces $X,Y$, respectively gives quasi-component in the product space $X\times Y$. If spaces $X,Y$ are locally-compact, paracompact and Haussdorf then we prove that space of quasi-components of the product $Q(X\times Y)$ is homeomorphic with the product space $Q(X) \times Q(Y) $, so these two spaces have the same topological properties.